Indispensable digits for digit sums

Ji Young Choi
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 2, Pages 40-48
DOI: 10.7546/nntdm.2019.25.2.40-48
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Authors and affiliations

Ji Young Choi

Department of Mathematics, Shippensburg University of PA
1871 Old Main Dr., Shippensburg PA 17257, United States

Abstract

Let b be an integer greater than 1 and g = b − 1. For any nonnegative integer n, we define indispensable digits in the base-b representation of n so that we can calculate the digit sum of the base-b representation of g · n: Instead of adding every digit in it, we multiply g by the number of the indispensable digits in the base-b representation of n. Then, we find the formula to calculate the digit sum of g · n + r using the number of indispensable digits in n, for any nonnegative integers n and r with 0 < r < g.

Keywords

  • Digit sum
  • Indispensable digits
  • Digit sum congruence
  • Casting out nines
  • Divisibility test

2010 Mathematics Subject Classification

  • 11A63
  • 11A07

References

  1. Atanassov, K. (1985). An arithmetic function and some of its applications, Bull. of Number Theory and Related Topics, 9, 18–27.
  2. Atanassov, K. (2015). A digital arithmetical function and some of its applications, Proceedings of the Jangjeon Mathematical Society, 18 (4), 511–528.
  3. Datta, D. & Singh, A. N. (1962). History of Hindu Mathematics: A Source Book, Asia Publishing House, Bombay, Available online at: https://ia801600.us.archive.org/20/items/HinduMathematics/HinduMathematics.pdf.
  4. Shallit, J. (2009). A Second Course in Formal Languages and Automata Theory, Cambridge Universisty Press, New York.
  5. Weisstein, E. W. MathWorld-A Wolfram Web Resource, Available online at: http://mathworld.wolfram.com/DigitSum.html.

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Cite this paper

APA

Choi, J. Y. (2019). Indispensable digits for digit sums. Notes on Number Theory and Discrete Mathematics, 25(2), 40-48, doi: 10.7546/nntdm.2019.25.2.40-48.

Chicago

Choi, Ji Young “Indispensable digits for digit sums.” Notes on Number Theory and Discrete Mathematics 25, no. 2 (2019): 40-48, doi: 10.7546/nntdm.2019.25.2.40-48.

MLA

Choi, Ji Young “Indispensable digits for digit sums.” Notes on Number Theory and Discrete Mathematics 25.2 (2019): 40-48. Print, doi: 10.7546/nntdm.2019.25.2.40-48.

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